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phy127:hw3 [2011/02/21 13:54] mvfernandezserra |
phy127:hw3 [2011/02/21 13:56] (current) mvfernandezserra |
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We have a nonconducting sphere, with a total charge Q uniformly distributed throughout its volume. The E field inside the sphere is | We have a nonconducting sphere, with a total charge Q uniformly distributed throughout its volume. The E field inside the sphere is | ||

not zero, because it is not a conductor and there is charge everywhere inside. We define to regions: r<r0 (inside) and r>ro (outside).\\ | not zero, because it is not a conductor and there is charge everywhere inside. We define to regions: r<r0 (inside) and r>ro (outside).\\ | ||

- | We also make use of the charge density instead of the total charge: $\sigma=\frac{Q}{4/3\pir_0^3}$\\ | + | We also make use of the charge density instead of the total charge: $\sigma=\frac{Q}{4/3\pi r_0^3}$\\ |

Inside, r<r0:\\ | Inside, r<r0:\\ | ||

Line 95: | Line 95: | ||

We need to integrate the potential due to a differential of charge $d$q. $V=\int{\frac{\partial q}{4\pi\epsilon_0 r}}$.\\ | We need to integrate the potential due to a differential of charge $d$q. $V=\int{\frac{\partial q}{4\pi\epsilon_0 r}}$.\\ | ||

$r=l/\pi$\\ | $r=l/\pi$\\ | ||

- | $V=\frac{\pi}{4\pi\epsilon_0 l}\inr \partial q=\frac{Q}{4\epsilon_0 l}$.\\ | + | $V=\frac{\pi}{4\pi\epsilon_0 l}\int\partial q=\frac{Q}{4\epsilon_0 l}$.\\ |

==== 23.61==== | ==== 23.61==== | ||

- | $\frac{v_e}{v_p}=sqrt{\frac{m_p}{m_e}}$ | + | $\frac{v_e}{v_p}=\sqrt{\frac{m_p}{m_e}}$ |

==== 23.71==== | ==== 23.71==== | ||

==== 23.84==== | ==== 23.84==== |